Drupal 6 is stable and it has a lot of great features that aren't available in Drupal 5. The only reason I would use Drupal 5 for a new site is if using a module that were only available for Drupal 5. Ubercart is one that comes to mind. (I haven't used Ubercart, but it was recommended to me as the ideal way to to ecommerce in Drupal.)
Drupal 6 is great. There's no reason not to use it except if there is a module that isn't available yet. I can't think of any modules that I use on a regular basis that aren't available for Drupal 6.
Drupal 6 gives you things like:
More AJAX - you can drag & drop things to order them instead of setting weights by numbers in select boxes.
Views 2 - this version of the Views module is incredible, and only available for Drupal 6.
Trigger and Actions - built in.
Status updates - Drupal 6 emails you when new versions of your installed modules are available.
and much more...